Extended equation for description of nonlinear waves in liquid with gas bubbles
, 2013 Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves.
Kudryashov, Nikolai A. +1 more
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On stabilization of small solutions in the nonlinear Dirac equation with a trapping potential [PDF]
, 2016 We consider a Dirac operator with short range potential and with eigenvalues. We add a nonlinear term and we show that the small standing waves of the corresponding nonlinear Dirac equation (NLD) are attractors for small solutions of the NLD.
Cuccagna, Scipio, Tarulli, Mirko
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KdV-type equations linked via Baecklund transformations: remarks and perspectives
, 2018 Third order nonlinear evolution equations, that is the Korteweg-deVries (KdV), modified Korteweg-deVries (mKdV) equation and other ones are considered: they all are connected via Baecklund transformations.
Carillo, Sandra
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Two-point method for solving nonlinear equation with nondifferentiable operator (in Ukrainian) [PDF]
Математичні Студії, 2011 In the paper we study a combined differential-difference method for solving nonlinear equations with non-differentiable operator. The semilocal convergence of the method is investigated and the order of convergence is established.
S. M. Shakhno, H. P. Yarmola
doaj
Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side
Mathematical Modelling and Analysis, 2015 In this paper we deal with the problem of asymptotic integration of a class of fractional differential equations of the Caputo type. The left-hand side of such type of equation is the Caputo derivative of the fractional order r ∈ (n − 1, n) of the ...
Milan Medved, Michal Pospisil
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Higher-order corrections to the short-pulse equation
, 2012 Using renormalization group techniques, we derive an extended short- pulse equation as approximation to a nonlinear wave equation. We investigate the new equation numerically and show that the new equation captures efficiently higher- order effects on ...
Agrawal G P +12 more
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Fast and accurate modelling of nonlinear pulse propagation in graded-index multimode fibers [PDF]
, 2017 We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists in a 1+1D generalized nonlinear Schr\"odinger equation with a periodic nonlinear coefficient, which ...
Arabi, Carlos Mas +3 more
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Local convergence of some high order iterative methods based on the decomposition technique using only the first derivative [PDF]
Surveys in Mathematics and its Applications, 2017 We present a local convergence analysis of some high order iterative methods based on the decomposition technique using only the first derivative for solving equations in order to approximate a solution of a nonlinear equation.
Ioannis K. Argyros, Santhosh George
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Local Convergence of Exquerro-Hernandez Method
Annals of the West University of Timisoara: Mathematics and Computer Science, 2016 Local convergence of Ezquerro-Hernandez iteration is investigated in the setting of finite dimensional spaces. A procedure to estimate the local convergence radius for this iteration is proposed.
Măruşter Ştefan
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Extending the Applicability of Two-Step Solvers for Solving Equations
Mathematics, 2019 We present a local convergence of two-step solvers for solving nonlinear operator equations under the generalized Lipschitz conditions for the first- and second-order derivatives and for the first order divided differences.
Ioannis K. Argyros, Stepan Shakhno
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